The Laplacian on a Riemannian Manifold: An Introduction to Analysis on Manifolds

By S. Rosenberg. 1997

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Geometric Deep Learning: Going beyond Euclidean data (2016, background): “Similarly, the intrinsic divergence is an operator div : L(2)(TX ) → L(2)(X ) acting on tangent vector fields and (formal) adjoint to the gradient operator [71],”
Diving into the shallows: a computational perspective on large-scale shallow learning (2017, background): “Let ks(x, z) be the heat kernel on the circle [Ros97].”
Graph embedding discriminant analysis on Grassmannian manifolds for improved image set matching (2011, unknown): “We note that more complex similarity graphs, like heat kernel graphs, can also be used to encode distances between points on Grassmannian manifolds [20].”
Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks (2021, background): “The simplicial Hodge Laplacian (Barbarossa & Sardellitti, 2020; Schaub et al., 2020), a discrete counterpart of the Laplacian operator in Hodge–de Rham theory (Rosenberg, 1997), provides a connection with the theory of spectral analysis and signal processing on these higher-dimensional domains.”
Shape‐from‐Operator: Recovering Shapes from Intrinsic Operators (2015, background): “A well-known fact in differential geometry is that the Laplace-Beltrami operator is fully determined by the Riemannian metric [Ros97], and, conversely, the metric is determined by the Laplace-Beltrami operator (or a heat kernel constructed from it) [ZGLG12].”